Overview
This lecture introduces engineering notation, a system for expressing very large or small numbers using standardized prefixes, making them easier to read, write, and understand—an essential skill in technical fields.
Purpose of Engineering Notation
- Engineering notation simplifies writing, reading, and conceptualizing very large or small numbers.
- It uses prefixes to replace long strings of zeros, making magnitude easy to distinguish.
- Proper use is critical for anyone in engineering or technical careers.
Prefixes for Large Numbers
- Numbers grouped in thousands (three-digit increments) match natural comma use in large numbers.
- Common prefixes:
- Kilo (k) = 10³ = 1,000
- Mega (M) = 10⁶ = 1,000,000
- Giga (G) = 10⁹ = 1,000,000,000
- Tera (T) = 10¹² = 1,000,000,000,000
- Coefficient (number before the prefix) should be ≥1 and <1,000.
Prefixes for Small Numbers
- Small numbers use negative powers of ten and similar three-digit groupings.
- Common prefixes:
- Milli (m) = 10⁻³ = 0.001
- Micro (μ or u) = 10⁻⁶ = 0.000001
- Nano (n) = 10⁻⁹ = 0.000000001
- Pico (p) = 10⁻¹² = 0.000000000001
Converting to Engineering Notation
- Move the decimal in steps of three (left for large, right for small numbers) to select the appropriate prefix.
- Ensure the coefficient is between 1 and 1,000.
- Examples:
- 2,200 ohms → 2.2 kiloohms
- 0.00002 amps → 20 microamps
- 0.000000033 farads → 33 picofarads
Using Engineering Prefixes for Comparison
- Ignore the coefficient; compare prefixes to quickly assess magnitude.
- Order of magnitude is clear: each prefix is 1,000 times larger or smaller than the next.
- Only compare coefficients when prefixes are the same.
Key Terms & Definitions
- Engineering Notation — A method of expressing numbers using multiples of 1,000 with standard prefixes.
- Coefficient — The numeric part before the prefix (should be ≥1 and <1,000).
- Prefix — A symbol indicating a power of 10, used to replace zeros.
- Base Unit — The standard unit without a prefix.
Action Items / Next Steps
- Memorize the key engineering prefixes and their values.
- Practice converting numbers to and from engineering notation.
- Review any provided prefix tables and examples.
- Prepare for upcoming lectures on calculator use and conversions between prefixes.